Question

Find the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ which passes through the points (3,0) and

(3$\sqrt{2}$,2).

Answer 1

The hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ passes through the points $(3,0)$ and $(3\sqrt{2},2)$.

So, $a^2=9$ and $b^2=4$

We know,

$b^2=a^2(e^2-1)$

$e^2=\frac{13}{9}$

$e=\frac{\sqrt{13}}{3}$